<== an equilateral triangle
split into two equal triangles. These are called 30˚-60˚
right triangles. Why? Well,
an equilateral triangle has all angles equal to 60˚. When we put the
height in, it split the top angle in half, into two 30˚ angles. So, in one
of the right triangles, there is a 90˚ angle, a 60˚ angle, and a 30˚ angle.

Now let's say we want to find the height of the equilateral
triangle (the side b of the small right triangle). First use the
Pythagorean Theorem.

a2 + b2 = c2b2 = c2 - a2

b2 = 22 - 12b2 = 4 - 1
b2 = 3
b = √3 or 1√3

Let's try it again if the side
length of the equilateral triangle is 4.

b2 = c2 - a2

b2 = 42 - 22b2 = 16 - 4
b2 = 12
b = √12 = 2√3

Notice a pattern? :) ... if you
don't, the rule is below:

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In a 30˚-60˚ right
triangle, if the smallest side is a units, then the hypotenuse will be 2a units,
and the longer side will be a√3 units.

Similarly, if the
side length of an equilateral triangle is a units, then the height will be Ża√3
units.

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